Some people will just not "do" politics properly. Look – a couple of hundred people in tents who do not know their place! Why are they not outside a bad bank? Their demands are too muddled. Best ignore them. Remember the students? They protested about fees because that's just what students do. Best patronise them. What about the rioters? They were all criminals and nothing to do with politics at all. Best jail them.

This wave of unrest exists outside conventional politics and is just made for armchair cynics to sneer at. The Labour party mumbles apologetically when it should understand what is happening.

The line of all political parties is basically that we don't want our public spaces cluttered up with people or placards. If you want to make your quaint objections to capitalism, form an orderly queue. In other words, go on a demonstration. Despite the million-long queue that was the anti-Iraq war demonstration, the politicians knew best and took us into battle.

This may be why occupations are the new demos. About time. I am with Howard Zinn. Our problems are caused by too much obedience rather than civil disobedience. When leaders lose authority, people begin to take charge themselves.

This is why when the media visit the camp outside St Paul's, they are bowled over by the ability of protesters to organise themselves: food tents, library tents, lectures. All of this has been put in place very quickly with the aid of the techies who flocked there and helped enable an enviable PR operation. The same was true of student occupations. They were impressive.

What used to take weeks can now be done in a day. Anyone who was at Greenham Common knows how hard it was to organise an occupation before mobiles existed. I mention Greenham not out of any deep nostalgia but because rather than read across these protests internationally – St Paul's is not Tahrir Square or Syntagma Square – we can look at our own recent history.

Greenham functioned largely as a symbolic protest. We lost but we learned how to produce a spectacle. Unlike the current Occupy London the demand was not at all vague. We did not want cruise missiles. But like the new occupations, it functioned both as a political learning curve and a magnet for eccentrics. My favourite was a woman we used to call Metal Micky who wore a belt of bolt-cutters and had come to the conclusion that metal itself was a phallocentric conspiracy. Yes, actual metal. As a part-timer, I was only ever there for a day or so, and so I was not in a position to challenge this "belief". Apart from having a job, I also could not stick the endless self-organisation and divvying up of tasks, so I admire anyone who can. Without hierarchies, the simplest thing is immense and what with this and the ululating and shining mirrors to reflect back the evil of the military-industrial complex, I was exhausted.

The men around us at that time – let's call them anarchists – were a bit jealous so they decided to Stop the City. They did indeed want to smash up capitalism, not just tamper at the edges. This demonstration in 1984 was billed as a "carnival against war, oppression and destruction". It sounds nice and vague. It got nasty. The police moved in to blockade us. I got out as the horses came in because I was pregnant at the time. Certainly, what I saw at those demos was the birth of kettling. And some say the beginnings of the anti-globalisation movement.

Much damage was caused and lots of arrests were made but my point is that the idea of targeting the City of London – the financial centre, not Westminster – is not new. Those who make that quip attributed to Wilde about "the problem with socialism is that it takes too many evenings" have never been around anarchists. It takes weeks to decide who makes the tea. Yet the image of anarchy remains that of chaos when it is mostly "forums". When there are no leaders, the practice, not simply the theory, of protest becomes at times an extraordinarily creative but draining political education. We hardly need Žižek to reheat Althusser to tell us this.

That is one of the reasons why the Occupations are energising those who visit. They have "got it together". Structures for collective decision- making are in place, if clunky.

Indeed 200 or so people in tents appear to have created an organisation that can act more effectively than the Church of England. Though this was never meant to be a clash with the church, it seems entirely suitable. When politics fails – and it has with the banks – we end up talking about morality. The church has now finally decided that some of the most extreme practices of neo-liberalism – the selling on of bundles of risk by rich people paid for with the homes and jobs of poor people – is not morally healthy. Who knew?

The church has had its consciousness raised. Or at least it has been prodded awake. This new movement is not going to suddenly reform the banking system, but is conventional politics? Write these protesters off if you like. As we did the rioters. To connect the two is still verboten. For these are uncertain times. Anarchy never feels safe. For anarchy is, in reality, a process by which people begin to feel their own power. Maybe just for one day. Maybe for the first time. If this is not "political" I don't know what is.

After a mainly peaceful day-long protest by thousands of demonstrators in Oakland, California, several hundred people rallied through the night, painting graffiti, breaking windows and setting fire to rubbish